Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 78
Number of page(s) 24
DOI https://doi.org/10.1051/cocv/2023062
Published online 08 November 2023
  1. E. Acerbi, G. Bouchitté and I. Fonseca, Relaxation of convex functionals: the gap phenomenon. Ann. Inst. Henri Poincare (C) Anal. Non Lineaire 20 (2003) 359–390. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Acerbi and G. Mingione, Regularity results for a class of quasiconvex functionals with nonstandard growth. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 30 (2001) 311–339. [MathSciNet] [Google Scholar]
  3. E. Acerbi and G. Mingione, Regularity results for a class of functionals with nonstandard growth. Arch. Rational Mech. Anal. 156 (2001) 121–140. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Almi, D. Reggiani and F. Solombrino, Lower semicontinuity and relaxation for free discontinuity functionals with nonstandard growth, arXiv:2301.07406 (2023). [Google Scholar]
  5. L. Ambrosio, A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B 3 (1989) 857–881. [MathSciNet] [Google Scholar]
  6. L. Ambrosio, Existence theory for a new class of variational problems. Arch. Rat. Mech. 111 (1990) 291–322. [CrossRef] [Google Scholar]
  7. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  8. S. Campanato, Proprietà di hölderianità di alcune classi di funzioni. Ann. Scuola Norm. Sup. Pisa CL Sci. 17 (1963) 175–188. [MathSciNet] [Google Scholar]
  9. M. Carriero and A. Leaci, Sk-valued maps minimizing the Lp norm of the gradient with free discontinuities. Ann. Scuola Normale Superiore Pisa - Classe Sci. 18 (1991) 321–352. [MathSciNet] [Google Scholar]
  10. Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66 (2006) 1383–1406. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Coscia and G. Mingione, Hölder continuity of the gradient of p(x)-harmonic mappings. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 363–368. [CrossRef] [MathSciNet] [Google Scholar]
  12. V. De Cicco, C. Leone and A. Verde, Lower semicontinuity in SBV for integrals with variable growth. SIAM J. Math. Anal. 42 (2010) 3112–3128. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. De Giorgi, Teoremi di semicontinuità nel calcolo delle variazioni, Lezioni tenute all’Istituto Nazionale di Alta Matematica, a.a. 1968–1969, Roma (1969). [Google Scholar]
  14. E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195–218. [CrossRef] [MathSciNet] [Google Scholar]
  15. L. Diening, Maximal function on generalized Lebesgue spaces Lp(·). Math. Inequal. Appl. 7 (2004) 245–253. [MathSciNet] [Google Scholar]
  16. L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, Springer (2010). [Google Scholar]
  17. L. Diening, J. Malek and M. Steinhauer, On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications. ESAIM Control Optim. Calc. Var. 14 (2008) 211–232. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  18. L. Diening and S. Schwarzacher, Global gradient estimates for the p(·)-Laplacian. Nonlinear Anal. 106 (2014) 70–85. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Eleuteri and A. Passarelli di Napoli, Lipschitz regularity of minimizers of variational integrals with variable exponents. Nonlinear Anal.: Real World Applic. 71 (2023) 103815. [CrossRef] [Google Scholar]
  20. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992). [Google Scholar]
  21. I. Fonseca, and N. Fusco, Regularity results for anisotropic image segmentation models. Ann. Scuola Norm. Super. Pisa-Cl. Sci. 24 (1997) 463–499. [Google Scholar]
  22. I. Fonseca, and N. Fusco, P. Marcellini, An existence result for a nonconvex variational problem via regularity. ESAIM: Control Optim. Calc. Var. 7 (2002) 69–95. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  23. G.A. Francfort and J.J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Friedrich, A compactness result in GSBVp and applications to Γ-convergence for free discontinuity problems. Calc. Var. 58 (2019) 86. [CrossRef] [Google Scholar]
  25. N. Fusco, and G. Mingione, C. Trombetti, Regularity of minimizers for a class of anisotropic free discontinuity problems. J. Convex Anal. 8 (2001) 349–367. [MathSciNet] [Google Scholar]
  26. E. Giusti, Direct Methods in the Calculus of Variations. World Scientific Publishing Co., Inc., River Edge (2003). [CrossRef] [Google Scholar]
  27. A.A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. London 221 (1921) 163–198. [CrossRef] [Google Scholar]
  28. P. Harjulehto, P. Hästö and V. Latvala Minimizers of the variable exponent, non-uniformly convex Dirichlet energy. J. Math. Pures Appl. 89 (2008) 174–197. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Harjulehto, P. Hästö, V. Latvala and O. Toivanen, Critical variable exponent functionals in image restoration. Appl. Math. Lett. 26 (2013) 56–60. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Hästö and J. Ok, Maximal regularity for local minimizers of non-autonomous functionals. J. Eur. Math. Soc. 24 (2022) 1285–1334. [Google Scholar]
  31. O. Kovácik and J. Rákosník, On spaces Lp(x) and W1,p(x). Czechoslovak Math. J. 41 (1991) 592–618. [CrossRef] [MathSciNet] [Google Scholar]
  32. F. Li, Z. Li and L. Pi, Variable exponent functionals in image restoration. Appl. Math. Comput. 216 (2010) 870–882. [MathSciNet] [Google Scholar]
  33. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42 (1989) 577–685. [CrossRef] [Google Scholar]
  34. G. Scilla, F. Solombrino and B. Stroffolini, Integral representation and Γ-convergence for free-discontinuity problems with p(·)-growth. Calc. Var. 62 (2023) 213. [CrossRef] [Google Scholar]
  35. I.I. Sharapudinov, Approximation of functions in the metric of the space Lp(t)([a,b]) and quadrature formulas (in Russian), in Constructive Function Theory’81 (Varna, 1981), 189–193. Publ. House Bulgar. Acad. Sci., Sofia (1983). [Google Scholar]
  36. V.V. Zhikov, Problems of convergence, duality, and averaging for a class of functionals of the calculus of variations. Dokl. Akad. Nauk SSSR 267 (1982) 524–528. [MathSciNet] [Google Scholar]
  37. V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory. Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986) 675–710. [MathSciNet] [Google Scholar]
  38. V.V. Zhikov, On some variational problems. Russ. J. Math. Phys. 5 (1997) 105–116. [Google Scholar]

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